Solve for $x>0$ in the following arithmetic sequence: $1^2, x^2, 3^2, \ldots$.
The term $x^2$ is simply the average of $1^2 = 1$ and $3^2 = 9$, so $x^2 = (1 + 9)/2 = 5$.  Because $x > 0$, $x = \boxed{\sqrt{5}}$.